License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2020.21
URN: urn:nbn:de:0030-drops-122687
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12268/
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Chaplick, Steven ; Förster, Henry ; Kryven, Myroslav ; Wolff, Alexander

Drawing Graphs with Circular Arcs and Right-Angle Crossings

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LIPIcs-SWAT-2020-21.pdf (0.9 MB)

Abstract

In a RAC drawing of a graph, vertices are represented by points in the plane, adjacent vertices are connected by line segments, and crossings must form right angles. Graphs that admit such drawings are RAC graphs. RAC graphs are beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n-10 edges.
We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Turán-type result showing that an arc-RAC graph with n vertices has at most 14n-12 edges and that there are n-vertex arc-RAC graphs with 4.5n - O(√n) edges.

BibTeX - Entry

@InProceedings{chaplick_et_al:LIPIcs:2020:12268,
  author =	{Steven Chaplick and Henry F{\"o}rster and Myroslav Kryven and Alexander Wolff},
  title =	{{Drawing Graphs with Circular Arcs and Right-Angle Crossings}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Susanne Albers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12268},
  URN =		{urn:nbn:de:0030-drops-122687},
  doi =		{10.4230/LIPIcs.SWAT.2020.21},
  annote =	{Keywords: circular arcs, right-angle crossings, edge density, charging argument}
}

Keywords: circular arcs, right-angle crossings, edge density, charging argument
Collection: 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
Issue Date: 2020
Date of publication: 12.06.2020

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